Divide. \[ \frac{24}{6} \div \frac{8}{9} \]

Step 1 ：Rewrite the division of fractions as a multiplication of the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator. So, the reciprocal of \(\frac{8}{9}\) is \(\frac{9}{8}\). Therefore, the problem can be rewritten as \(\frac{24}{6}\) * \(\frac{9}{8}\).

Step 2 ：Calculate the value of the first fraction \(\frac{24}{6}\), which is 4.0.

Step 3 ：Calculate the value of the second fraction \(\frac{8}{9}\), which is approximately 0.8888888888888888.

Step 4 ：Find the reciprocal of the second fraction, which is \(\frac{9}{8}\) or approximately 1.125.

Step 5 ：Finally, multiply the value of the first fraction by the reciprocal of the second fraction. The result of the multiplication is 4.5.

Step 6 ：The final answer is \(\boxed{4.5}\).